Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 7 - Estimates and Sample Sizes - 7-3 Estimating a Population Mean - Beyond the Basics: 39

Answer

μ is between -25.46 and 106.04. We can see that the outlier really affects the interval, so normally it should be removed when constructing such an interval.

Work Step by Step

The mean can be counted by summing all the data and dividing it by the number of data: $\frac{300+6.5+...+17.5}{10}=40.75.$ Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(300-40.75)^2+...+(17.5-40.75)^2}{9}}=91.28.$ $\alpha=1-0.95=0.05.$ $\sigma$ is unknown, hence we use the t-distribution with $df=sample \ size-1=10-1=9$ in the table. $t_{\alpha/2}=t_{0.025}=2.262.$ Margin of error:$t_{\alpha/2}\cdot\frac{s}{\sqrt {n}}=2.262\cdot\frac{91.28}{\sqrt{10}}\approx65.29.$ Hence the confidence interval:$\mu$ is between 40.75-65.29=-25.46 and 40.75+65.29=106.04. We can see that the outlier really affects the interval, so normally it should be removed when constructing such an interval.
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